Abstract
Infrared singularities arising in some renormalized amplitudes of quantum electrodynamics are analyzed using the dimensional regularization method. We define infrared and ultraviolet convergent regions in the ν complex plane (ν is the number of dimensions of space time). It turns out that these regions do not overlap for quantum electrodynamics. Nevertheless, it is shown that there exists a unique analytic continuation from the infrared convergent region which allows us to interpret the infrared divergence in the renormalized electron self-energy amplitude as an isolated singularity at ν = 4. This statement seems to be true at all orders of perturbation theory. We also prove that the double limit μ → 0, ν → 4 (μ is the auxiliary photon mass) does not exist in quantum electrodynamics and we conjecture that this lack of uniformity provides theoretical support for the ansatz of Marciano and Sirlin.
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